In general, vehicle yaw rate control systems determine a desired yaw rate based on driver steering angle and other parameters, develop a yaw rate control command, and selectively brake one or more vehicle wheels in accordance with the yaw rate control command so that the vehicle achieves the desired yaw rate. In open-loop systems, the yaw rate control command is determined primarily as a function of the desired yaw rate, whereas in closed-loop systems, the yaw rate control command is determined primarily as a function of the difference, or error, between the desired yaw rate and a measure or estimate of the actual yaw rate. In either type of system, the determination of the desired yaw rate is based on an assumption that the vehicle is operating on dry pavement--that is, a surface having a high lateral coefficient of adhesion. Thus if the surface adhesion capability is not taken into account, the desired yaw rate can easily exceed the surface adhesion capability when the vehicle is operating on a slippery surface such as snow. In such circumstances, the yaw rate control will not be optimal.
Two different approaches for addressing reduction in surface adhesion capability have been considered. The simplest approach is to reduce the control gains, but this also reduces the overall aggressiveness of the control, and is often not favored. The second approach is to estimate the surface adhesion capability during a steering maneuver based on a measure of instantaneous lateral acceleration, and to dynamically limit the desired yaw rate accordingly. While this approach works well when the steering input is substantially constant, it does not work well during transient steering because the desired yaw rate and the lateral acceleration (and therefore, the surface adhesion estimate) are not in phase with each other. This phenomenon can be seen in the graph of FIG. 4A, which depicts a yaw rate limit based on lateral acceleration (solid trace) with the desired yaw rate (broken trace) during a transient steering maneuver on a low adhesion surface. As soon as the steering begins to change significantly, the desired yaw rate begins to lead the yaw rate limit, to the point of being completely out of phase. Accordingly, the robustness of the second approach is limited.